# Graph Signal Processing for Geometric Data and Beyond: Theory and Applications

arXiv: https://arxiv.org/abs/2008.01918 · HTML: https://mlsanity.com/paper/2008.01918/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2020.

## Built on by (most cited first, 23 of 23)

- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Parameter-Efficient Fine-Tuning in Spectral Domain for Point Cloud Learning](https://mlsanity.com/paper/2410.08114/) (2024)
- [Imperceptible Transfer Attack and Defense on 3D Point Cloud Classification](https://mlsanity.com/paper/2111.10990/) (2021)
- [Density-Insensitive Unsupervised Domain Adaption on 3D Object Detection](https://mlsanity.com/paper/2304.09446/) (2023)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Deep Point Set Resampling via Gradient Fields](https://mlsanity.com/paper/2111.02045/) (2021)
- [SCTN: Sparse Convolution-Transformer Network for Scene Flow Estimation](https://mlsanity.com/paper/2105.04447/) (2021)
- [Exploring the Devil in Graph Spectral Domain for 3D Point Cloud Attacks](https://mlsanity.com/paper/2202.07261/) (2022)
- [Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing](https://mlsanity.com/paper/2207.13326/) (2022)
- [3DHacker: Spectrum-based Decision Boundary Generation for Hard-label 3D Point Cloud Attack](https://mlsanity.com/paper/2308.07546/) (2023)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches](https://mlsanity.com/paper/2208.14160/) (2022)
- [Perception-Guided Quality Metric of 3D Point Clouds Using Hybrid Strategy](https://mlsanity.com/paper/2407.03885/) (2024)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [Dynamic Point Cloud Denoising via Gradient Fields](https://mlsanity.com/paper/2204.08755/) (2022)
- [GeodesicPSIM: Predicting the Quality of Static Mesh with Texture Map via Geodesic Patch Similarity](https://mlsanity.com/paper/2308.04928/) (2023)
- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [STS-Mixer: Spatio-Temporal-Spectral Mixer for 4D Point Cloud Video Understanding](https://mlsanity.com/paper/2604.11637/) (2026)
- [StarNet: Style-Aware 3D Point Cloud Generation](https://mlsanity.com/paper/2303.15805/) (2023)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [Hard-Label Black-Box Attacks on 3D Point Clouds](https://mlsanity.com/paper/2412.00404/) (2024)
- [Transform-Aligned Learned Features for Lossy Point Cloud Attribute Compression](https://mlsanity.com/paper/2609.34834/) (2026)

## Abstract (arXiv)

Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to irregular sampling patterns of most geometric data, traditional image/video processing methodologies are limited, while Graph Signal Processing (GSP) -- a fast-developing field in the signal processing community -- enables processing signals that reside on irregular domains and plays a critical role in numerous applications of geometric data from low-level processing to high-level analysis. To further advance the research in this field, we provide the first timely and comprehensive overview of GSP methodologies for geometric data in a unified manner by bridging the connections between geometric data and graphs, among the various geometric data modalities, and with spectral/nodal graph filtering techniques. We also discuss the recently developed Graph Neural Networks (GNNs) and interpret the operation of these networks from the perspective of GSP. We conclude with a brief discussion of open problems and challenges.